Lakes of Wada

So imagine you have three fluids that don&#x27;t mix which are colored red, green, blue. You can make drops of these fluids on a piece of paper, and manipulate their shapes e.g. with a pipette.<p>This article is saying that mathematically, it&#x27;s possible to make three single, continuous but weirdly shaped drops of these fluids, that together fill a square, in a way such that if you consider the three drop outlines as seen from above (e.g. by a camera), they all have the same outline.

This entry needs a simple english page. I read the first paragraph and didn&#x27;t understand anything.

It is one counterexample in Topology for the Jordan Curve Theorem.

Wada basins exist for any number of open sets. As you could probably guess from the article, the Newton method applied to x^n - 1 gives a Wada basin of n sets. These are fun counterexamples to the claim &quot;given three nontrivial disjoint sets on a plane, their boundaries are not mutally equal.&quot;